(a+1)+(2a+2)+(3a+3)+(4a+4)=5

Solution for (a+1)+(2a+2)+(3a+3)+(4a+4)=5 equation:

Simplifying
(a + 1) + (2a + 2) + (3a + 3) + (4a + 4) = 5

Reorder the terms:
(1 + a) + (2a + 2) + (3a + 3) + (4a + 4) = 5

Remove parenthesis around (1 + a)
1 + a + (2a + 2) + (3a + 3) + (4a + 4) = 5

Reorder the terms:
1 + a + (2 + 2a) + (3a + 3) + (4a + 4) = 5

Remove parenthesis around (2 + 2a)
1 + a + 2 + 2a + (3a + 3) + (4a + 4) = 5

Reorder the terms:
1 + a + 2 + 2a + (3 + 3a) + (4a + 4) = 5

Remove parenthesis around (3 + 3a)
1 + a + 2 + 2a + 3 + 3a + (4a + 4) = 5

Reorder the terms:
1 + a + 2 + 2a + 3 + 3a + (4 + 4a) = 5

Remove parenthesis around (4 + 4a)
1 + a + 2 + 2a + 3 + 3a + 4 + 4a = 5

Reorder the terms:
1 + 2 + 3 + 4 + a + 2a + 3a + 4a = 5

Combine like terms: 1 + 2 = 3
3 + 3 + 4 + a + 2a + 3a + 4a = 5

Combine like terms: 3 + 3 = 6
6 + 4 + a + 2a + 3a + 4a = 5

Combine like terms: 6 + 4 = 10
10 + a + 2a + 3a + 4a = 5

Combine like terms: a + 2a = 3a
10 + 3a + 3a + 4a = 5

Combine like terms: 3a + 3a = 6a
10 + 6a + 4a = 5

Combine like terms: 6a + 4a = 10a
10 + 10a = 5

Solving
10 + 10a = 5

Solving for variable 'a'.

Move all terms containing a to the left, all other terms to the right.

Add '-10' to each side of the equation.
10 + -10 + 10a = 5 + -10

Combine like terms: 10 + -10 = 0
0 + 10a = 5 + -10
10a = 5 + -10

Combine like terms: 5 + -10 = -5
10a = -5

Divide each side by '10'.
a = -0.5

Simplifying
a = -0.5